Title :
Empirical analysis of computational and accuracy tradeoffs using compactly supported radial basis functions for surface reconstruction
Author :
Morse, Bryan ; Liu, Weiming ; Otis, Lauralea
Author_Institution :
Dept. of Comput. Sci., Brigham Young Univ., Provo, UT, USA
Abstract :
Implicit surfaces can be constructed from scattered surface points using radial basis functions (RBFs) to interpolate the surface´s embedding function. Many researchers have used thin-plate spline RBFs for this because of their desirable smoothness properties. Others have used compactly supported RBFs, leading to a sparse matrix solution with lower computational complexity and better conditioning. However, the limited radius of support introduces a free parameter that leads to varying solutions as well as varying computational requirements: a larger radius of support leads to smoother and more accurate solutions but requires more computation. This work presents an empirical analysis of this radius of support. The results using compactly supported RBFs are compared for varying model sizes and radii of support, exploring the relationship between data density and the accuracy of the interpolated surface.
Keywords :
computational complexity; computational geometry; image reconstruction; interpolation; radial basis function networks; sparse matrices; splines (mathematics); computational complexity; implicit surfaces; radial basis functions; sparse matrix; surface interpolation; surface reconstruction; Computational complexity; Computational efficiency; Computer science; Environmentally friendly manufacturing techniques; Equations; Scattering; Sparse matrices; Spline; Surface fitting; Surface reconstruction;
Conference_Titel :
Shape Modeling Applications, 2004. Proceedings
Print_ISBN :
0-7695-2075-8
DOI :
10.1109/SMI.2004.1314527